The kinematical evolution of four extreme ultraviolet waves, well observed by the Extreme Ultraviolet Imager on board the Solar-Terrestrial Relations Observatory (STEREO), is studied by visually tracking wave fronts as well as by a semi-automatized perturbation profile method, which leads to results matching each other within the error limits. The derived mean velocities of the events under study lie in the range of 220-350 km s–1. The fastest of the events (2007 May 19) reveals a significant deceleration of – 190 m s–2, while the others are consistent with a constant velocity during wave propagation. The evolution of maximum-intensity values reveals initial intensification of 20%-70% and decays to original levels within 40-60 minutes, while the widths at half-maximum and full-maximum of the perturbation profiles broaden by a factor of two to four. The integral below the perturbation profile remains basically constant in two cases, while it shows a decrease by a factor of three to four in the other two cases. From the peak perturbation amplitudes, we estimate the corresponding magnetosonic Mach numbers M ms, which range from 1.08-1.21. The perturbation profiles reveal three distinct features behind the propagating wave fronts: coronal dimmings, stationary brightenings, and rarefaction regions. All features appear after the wave passage and only slowly fade away. Our findings indicate that the events under study are weak-shock fast-mode magnetohydrodynamic waves initiated by the CME lateral expansion.